The central problem of creating useful controllable nuclear fusion reactions among ions is the necessity of confining a sufficient density of ions over a large enough volume of space, with high enough particle energy, to ensure that the reaction rate density between the ions is high enough to be interesting for both power generation and to overcome all radiative, collisional and other losses that may be associated with or inherent in the fact of the particles' confinement at high energy. Traditionally, two principal means have been examined to attempt the achievement of these conditions. These are "inertial" confinement and "magnetic" confinement.
The major means of attempting inertial confinement has been the use of intense beams of laser light, focussed on the surface material of spheres made of or containing fusion fuels, with sufficient strength to vaporize, heat and "blow off" surface material and thus to provide a radial compressive force on the sphere surface. This force then can act to accelerate the sphere surface inwards, compressing and heating the material contained therein. If of sufficient strength this could, in principle, cause particle densities and temperatures (energies) to become high enough that fusion reactions may occur. The principal difficulty in this approach has been the attainment of stability during compression over a large enough volume of material, in a short enough time, that radiation and electron conduction losses do not dominate and prevent the achievement of the requisite conditions for fusion. This approach has not proven feasible to date, and is not of further interest here.
Most of the world's fusion research efforts have been devoted to the magnetic confinement approach, in which strong magnetic fields are used to constrain the motion of fusion fuel ions (and electrons) along closed field lines in toroidal field geometries, for example, or along open field lines with large internal magnetic reflection characteristics, as in double-ended "cusp" mirror or solenoidal magnetic "bottle" confinement schemes. In these approaches, the forces acting to "contain" or "confine" the fusion fuel ions are always due to the interaction of their motion with the externally-imposed magnetic fields, and are thus principally at right angles to the direction of the particle motion, rather than oppositely-directed, as would be desireable for action against the particle motion. These magnetic approaches thus suffer from use of an indirect and therefore inefficient means of constraining ion loss motion towards the confining walls of the system.
A more detailed discussion and summary of these and other related approaches to magnetic and non-electric inertial confinement of fusion fuel ions, and references to other writings on this topic is given by R. W. Bussard.sup.1 in U.S. Pat. No. 4,826,646, incorporated herein by reference, in connection with a description of an alternative electric inertial means of plasma confinement. This writing also describes the principal loss mechanisms confronting these "conventional" concepts for plasma confinement, and the general nature of the characteristics and limitations of these approaches.
In the above patent it is shown that conventional magnetic confinement approaches to fusion power generation are practically unable to take advantage of the large energy gains (G=ratio of energy output to energy input per fusion reaction) naturally found in the fusion reactions between various reactive isotopes of the light elements These gains can be as large as G.apprxeq.1000-2000 for the fusion of deuterium (D or .sup.2 H) with tritium (T or .sup.3 H), the two heavy isotopes of hydrogen (p or .sup.1 H), according to D+T.fwdarw..sup.4 He+.sup.o n (+17.6 MeV), or up to G.apprxeq.50-100 for fusion between hydrogen (p) and boron-11 (.sup.11 B), p+.sup.11 B.fwdarw.3 .sup.4 He (+8.6 MeV). In spite of this, it is found that the large power requirements for confinement and plasma heating in magnetic confinement approaches place practical engineering limits on the energy gain potentially achievable to 2&lt;G&lt;5.
Because of the difficulties inherent in the non-electric inertial and magnetic means for confining ions, some researchers turned to the use of more direct means of providing energy and motion to fusion fuels, by use of electric fields for their acceleration, and to spherically-convergent geometries for their densification by such motion. The simplest such system is that with pure spherical goemetry, in which a negative potential (-E.sub.w) is maintained at the center of a spherical shell by an electrode (cathode) mounted at the center. Positive ions introduced into this system will "fall down" the radial electric field toward the center, gaining energy and speed with nearly 100% efficiency in the process. In principle, this enables the achievement of large gain (G) from fusion reactions due to collisions at the system center.
If the ions are moving on purely radial paths, they will stop only when the force of electrostatic repulsion between them is sufficient to overcome the kinetic energy gained in their fall "down" the potential well. The radius (r.sub.coul) at which this will occur is very small for particles that have gained energy from potential wells with energy depths and densities of interest for fusion (e.g. for E.sub.w .apprxeq.100 keV, r.sub.coul .ltoreq.1E-5 cm), and a consequent large increase in density with decreasing radius will result from the geomet ric radius-squared variation of area in the converging ion flow.
However, a neutral (or near-neutral) plasma can not be confined by a static electric field of this type, because of charge separation and the resulting production of local dielectric fields that cancel the otherwise confining electrostatic field (Earnshaw's Theorem). Thus, the ion density that can be reached by this means is too small for fusion reactions at useful power levels. This difficulty can be overcome, and large ion densities achieved in plasmas of electrons and ions that are NOT locally neutral, by the use of inertial forces (particle kinetic energy) to create the confining field in a mixture of ions and electrons.
One of the earliest such concepts was studied by Elmore, Tuck and Watson.sup.2, in 1959, who proposed to overcome the Earnshaw's Theorem limits (above) by injection of energetic electrons radially inward to the center of a spherical volume through a spherical shell screen grid system, as indicated in FIG. 1a. The grid 100 is to be held at a high positive potential relative to an electron-emitting outer surface shell 110 surrounding the grid, so electrons are injected into the interior grid space with the energy of the potential difference 120 between the grid and the outer shell. Electrons thus injected will converge to a central region 130 where their electrostatic potential at the sphere center is approximately equal to the grid injection energy. FIG. 1b shows the potential distribution in such a device.
This large negative potential is then used to "trap" ions "dropped" into the well at the position of the electron injection grid 200, for ions so trapped will oscillate back and forth across the well at radius 200 (Rg) until central collisions result in fusion reactions, whose products 220 are sufficiently energetic to escape the well boundary, and deliver energy outside the well system. Non-reactive central collisions (i.e. scattering collisions) will not cause significant particle losses because they take place at the device center, where the only effect is to redirect the momentum vector of the colliding particles to new radial directions (assuming that the system is arranged so that central collisions have coincident center-of-mass and center-of-lab frames).
The system they studied was unpromising, however, because no means were provided to inhibit the loss of electrons from the sphere outer surface, and because the model for radial energy distribution of the electrons was such (Maxwellian) that very inefficient well formation was inherent in the system concept. These two defects led to greatly excessive electron power losses, such that net power production by fusion was a practical impossibility in this system. In addition both Elmore, Tuck and Watson.sup.2, and Furth.sup.3 showed that the confinement would be unstable at ion densities of interest for fusion power; thus ion confinement by electron injection in purely inertial-electrostatic wells, with the energy distributions assumed in these studies, is not a useful approach to the attainment of fusion power.
The limitations of electron injection were overcome by Farnsworth.sup.4 and Hirsch.sup.5, working with Farnsworth, who used ion injection rather than electron injection for the establishment of initial conditions for the formation of ion-trapping potential wells. The several-thousand-fold mass difference between these two species of charged particles allowed the attainment of much more stable field/ion-distribution structures than predicted for initial well formation by electron injection alone.
As shown in FIG. 2a, Hirsch and Farnsworth proposed to use the (radial) injection of (heavy) ions at well depth energies (hundreds of keV) to form a spherically-symmetric virtual anode region 300 within the injection volume, which would then attract electrons from an electron-emitting grid screen 310 located outside this volume, to fall radially through the ionic virtual anode and form a spherically-symmetric interior virtual cathode 320 which then, in turn, would accelerate the ions further to convergence at the system center 330.
In actual fact, however, their experiments utilized ion injection from six symmetrically-arranged ion "guns" 400 located in a cubical array around the surface of a sphere 410 which contained a screen grid 420 for electron emission (as described by Hirsch in two patents on the subject.sup.6), as shown in FIGS. 2b and 2c. These experiments achieved continuous fusion reaction rates of about 1E10 reactions/second, where EX designates 10 raised to the power X. The models used by Hirsch.sup.5 could not explain these high reaction rates (see e.g. Dolan et al.sup.7), and it was suspected that intersecting and colliding beam phenomena associated with the use of the tightly-focussed, opposing ion guns led to dominant phenomena different from those of the concentric, nested virtual electrode structures hypothesized by Hirsch/Farnsworth.sup.4,5 in their original descriptions of the concept.
Theoretical models of electron and ion circulation and of associated potential well shape were examined by Black.sup.8, who showed that the hypothesized virtual electrode structures would not occur in ion/electron flows which had any finite angular (i.e. transverse) momentum in their motion across the potential well. A later study by Baxter and Stuart.sup.9 of the Hirsch/Farnsworth experiments emphasized the role played by multiple (ca.7-10) transits of ions across the well due to the reflection of ions by grid structures from opposing ion guns used in the experiments, but still remained inconclusive as to an explanation for the anomalously large observed fusion neutron production rates.
In order to attain net power production (i.e. high gain, G) from fusion reactions induced by collisions at the center of such systems, Farnsworth, Hirsch and Bussard all showed that the electron current circulating across the system, and through the electron grid (virtual cathode) region, must reach very large values, equivalent to electron current recirculation ratios (G.sub.j) of G.sub.j .apprxeq.1E5 to 1E6 (circulating vs. injected electron current). The corollary ion flow recirculation ratio (G.sub.i) required was also shown to be in the range of G.sub.i .apprxeq.1E3 to 1E4, for the production of net fusion power. It is evident that these values can be attained only if electrons and/or ions are not removed by collisions with structure (e.g. grids) and/or walls of the system.
But in the Hirsch/Farnsworth approach, as in the concept of Elmore, et al above, the existence of grid structure of significant solidity in the path of the circulating particle flows will always prevent the buildup of these large circulating currents needed to obtain large system power gain (G) values. Thus an inherent limitation of the Hirsch/Farnsworth approach is due to the ion gun structures required for ion injection, and of associated electron-emitting grid structures to provide the gross charge neutralization required to allow buildup of large ion currents and of large densities of both ions and electrons in recirculating electron and ion flow, as needed for large system gain. The very components required for supply of particles to the system thus prevent the attainment of the high recirculating densities required for large power output.
This defect was recognized by Hirsch.sup.10, who tried to find a way to reduce structure-collision losses of electrons circulating through the system, by passing currents through the screen/grid wires or rods so as to provide "magnetic insulation" around them sufficient to prevent electrons from striking them as the electrons passed back and forth through the screen grid region. This did not appear to be promising, as proposed, for it introduced more complexity into the system structure and increased power requirements, without providing enough insulation to solve the structure-collision-loss problem. In addition, it introduced transverse momentum to the particle current streams, which further reduced their ability to converge towards a point by radial motion. Other work using electron injection to enhance magnetic confinement schemes was conducted by several researchers.sup.11, but is not relevant here.
In reference to FIGS. 3a and 3b, a solution to most of these problems was given by Bussard.sup.1,12 who proposed a concept for a magnetically-confined, electron-injection-driven, negative potential well, which confines ions 520 injected at low energy by injectors 530 on the field axes, principally by inertial-electrostatic fields set up by high-energy electrons 540, supplied by electron guns 510, and confines these electrons without structure-collisions by use of special polyhedral point-cusp quasi-spherical magnetic fields 500 around the system outer surface. FIG. 3a shows a cross-section of the polyhedral system of FIG. 3b, taken on the plane X--X. A detailed study of this concept.sup.13 shows that such a system can work, and that high gain values (and their requisite large electron current recirculation ratios, G.sub.j .apprxeq.1E5-1E6) can be obtained if special polyhedral surface magnetic fields of sufficient strength (e.g. 2-20 kGauss) are arranged around the system.
This concept and study was based on a general assumption of spherical convergence in ion and electron flow, with the ion motion at high convergence 610 dominated by ion transverse momentum content, and the electron motion inside a certain radius (the virtual cathode radius) dominated by the ion motion (the heavier ions pull the lighter electrons along, to avoid excessive positive charge buildup). Ion density increase with radial convergent motion under these conditions was taken to be varying approximately as 1/r.sup.2 to 1/r.sup.3, down to a (small) critical radius (r.sub.c) 620 at which ion radial motion had ceased, and all ion motion was then transverse and isotropic in a spherical surface sheet at that radius. This radius was shown to be determined by the average transverse momentum content of the ions at the system surface, after reaching steady-state from multiple traversals of the core, as compared with their radial momentum content at maximum radial speed (at well bottom). The ratio of critical radius to system radius (R) is then given by &lt;r.sub.c &gt;=(r.sub.c /R)=(E.sub.t /E.sub.r).sup.0.5, where E.sub.t and E.sub.r are mean transverse energy at the surface, and radial energy near the bottom of the potential well, respectively. System stability was assured by the large recirculating power flow, and by the existence of the externally-supplied polyhedral magnetic fields.
However, the limited density increase possible under these convergence scaling laws and conditions leads to requirements for large electron current recirculation ratios (G.sub.j &gt;1E5) which, in turn, require large quasi-spherical polyhedral surface fields 500 for electron confinement. Generation of these fields requires relatively large currents in the polyhedral windings 600 that define the magnet coil systems, and these lead to large ohmic power losses for use of normal conductors for the magnet coils. For use of DT fuels the losses are estimated as typically &gt;20-30 Mwe for systems with reasonable gain (G), while use of advanced fuels such as p.sup.11 B may require magnet coil power of &gt;60-100 Mwe for systems with minimally useful net gain.